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math.AP2001
On the Saddle Point Property of Abresch-Langer curves under the Curve Shortening Flow
Thomas Kwok-keung Au
In the study of the curve shortening flow on general closed curves, Abresch and Langer posed a conjecture that the homothetic curves can be regarded as saddle points between multi-…
math.AP2000
An Analysis on the Shape Equation for Biconcave Axisymmetric Vesicles
Thomas Kwok-keung Au, Tom Yau-heng Wan
We study the conditions on the physical parameters in the Helfrich bending energy of lipid bilayer vesicles. Among embedded surfaces with a biconcave axisymmetric shape, the variat…